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Recently, learning with soft labels has been shown to achieve betterperformance than learning with hard labels in terms of model generalization,calibration, and robustness. However, collecting pointwise labeling confidencefor all training examples can be challenging and time-consuming in real-worldscenarios. This paper delves into a novel weakly supervised binaryclassification problem called confidence-difference (ConfDiff) classification.Instead of pointwise labeling confidence, we are given only unlabeled datapairs with confidence difference that specifies the difference in theprobabilities of being positive. We propose a risk-consistent approach totackle this problem and show that the estimation error bound achieves theoptimal convergence rate. We also introduce a risk correction approach tomitigate overfitting problems, whose consistency and convergence rate are alsoproven. Extensive experiments on benchmark data sets and a real-worldrecommender system data set validate the effectiveness of our proposedapproaches in exploiting the supervision information of the confidencedifference.

Binary Classification with Confidence Difference